We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.
In this Letter we discuss theoretically the instabilities of thermotropic freely standing smectic-A films under shear flow\cite{re:wu}. We show that, in Couette geometry, the centrifugal force pushes the liquid crystal toward the outer boundary and induces smectic layer dilation close to the outer boundary. Under strong shear, this effect induces a layer buckling instability. The critical shear rate is proportional to $1/\sqrt{d}$, where $d$ is the thickness of the film.
Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, …
A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elast…
We employ kinetic Monte Carlo (KMC) simulations and a thin-film continuum model to comparatively study the transverse (i.e., Plateau-Rayleigh) instability of ridges formed by molecules on pre-patterned substrates. It is demonstrated that the evolution of the occurring instability qualitatively agrees between the two models for a single ridge as well as for two weakly interacting ridges. In particular, it is shown for both models that the instability occurs on well defined length and time scales which are, for the KMC model, significantly larger than the intrinsic scales of thermodynamic fluctu…
We consider solutions where the surface tension of the solvent is smaller than the surface tension of the polymer. In an evaporating film, a plume of solvent rich fluid, then induces a local depression in surface tension, and the surface forces tend to strengthen the plume. We give an estimate (at the level of scaling laws) for the minimum thickness required to obtain this instability. We predict that the thickness a) is a decreasing function of the solvent vapor pressure b) should be very small (<1 micron) provided that the initial solution is rather dilute. The overall evaporation time for t…
In both research and industrial settings spin coating is extensively used to prepare highly uniform thin polymer films. However, under certain conditions, spin coating results in films with non-uniform surface morphologies. Although the spin coating process has been extensively studied, the origin of these morphologies is not fully understood and the formation of non-uniform spincast films remains a practical problem. Here we report on experiments demonstrating that the formation of surface instabilities during spin coating is dependent on temperature. Our results suggest that non-uniform spin…
We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface, their motion also has a component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by three physical effects: the upward pushing f…
We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localised if its amplitude is taken …
The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the gas phase at rest, the dynamics of the vapour reduces to diffusion. The boundary condition at the interface couples transfer from the liquid to its vapour and diffusion flux. A non-local lubrication equation is obtained; this non-local nature comes from the Laplace equation associated with quasi-static diffusion. The linear stability of a flat film is studied …
Mechanical mapping of thin elastic films and living cells with spherical tip atomic force microscopy probes at large indentations
Institut de Bioenginyeria de Catalunya (IBEC), The Barcelona Institute of Science and Technology（加泰罗尼亚生物工程学院（IBEC），巴塞罗那科学技术研究所）；Departament d'Enginyeria Electrònica i Biomèdica, Universitat de Barcelona（巴塞罗那大学电子与生物医学工程系）；National Institute of Molecular Genetics (INGM)（分子遗传学国家研究所）；Department of Pharmaceutical Sciences, University of Milano（米兰大学药学系）
In this study, thin elastic films supported on a rigid substrate are brought into contact with a spherical glass indenter. Upon contact, adhesive fingers emerge at the periphery of the contact patch with a characteristic wavelength. Elastic films are also pre-strained along one axis before initiation of contact, causing the fingering pattern to become anisotropic and align with the axis along which the strain was applied. This transition from isotropic to anisotropic patterning is characterized quantitatively and a simple model is developed to understand the origin of the anisotropy.
We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to th…
Here, we report experimental results on the rupture of flat colloidal films over a large range of volume fractions, 0.00 $\le ϕ\le$ 0.47. The films are formed using a constant fluid volume, ruptured with a needle, and recorded using a high-speed camera. We show that colloidal films rupture in a manner quantitatively similar to Newtonian fluids, even well into the shear thinning regime. These results are consistent with the well-known mechanism of the rupture of Newtonian films, where the rupture rim rolls outward collecting more fluid and thus film rupture is a shear-free process. However, in …
Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.
Kinneyia are a class of microbially mediated sedimentary fossils. Characterised by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date there has been no conclusive explanation of the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a Kelvin-Helmholtz type instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the fi…
We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction performs rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity several characteristic instability modes can occur. In particular, rotational diffu…
We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient $Γ$. Being controlled by $Γ$, our model provides a unified framework to describe the long wavelength behaviour of a variety of thin polar-ordered systems, ranging from {\em wet} to {\em dry} active matters and free standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving…
Suppressed Rupture of Thin Metal Films via van der Waals Epitaxy
Peking University（北京大学）；Beijing University of Technology（北京工业大学）；National Center for Nanoscience and Technology（国家纳米科学中心）；Univ. Bordeaux, CNRS, LOMA, UMR 5798（波尔多大学，法国国家科学研究中心，LOMA实验室）
Ordered phases emerged in active suspensions of polar swimmers are under long-wavelength hydrodynamic mediated instabilities. In this letter, we show that chemical molecules dissolved in aqueous suspensions, as an unavoidable part of most wet active systems, can mediate long-range interactions and subsequently stabilize the ordered phases. Chemoattractant in living suspensions and dissolved molecules producing phoretic forces in synthesized Janus suspensions are reminiscent of such molecules. Communication between swimmers through the gradients of such chemicals generated by individual swimmer…
Microorganisms living in microfluidic environments often form multi-species swarms, where they can leverage collective motions to achieve enhanced transport and spreading. Nevertheless, there is a general lack of physical understandings of the origins of the multiscale unstable dynamics observed within these systems. Here, we build a computational model to study binary suspensions of rear- and front-actuated microswimmers, or respectively the so-called "pusher" and "puller" particles, that have different populations and swimming speeds. We perform direct particle simulations to reveal that col…
We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic liquid crystal films; however we note that similar instability mechanisms, and forms of the effective disjoining pressure, appear in other contexts, such as the well-studied problem of polymeric films on two-layered substrates. The analysis is carried out within the framework of the long-wave approximation, which leads to a fourth order nonlinear partial differen…
There are different ways for fluid flow to become turbulent, but usually many instabilities take place before that. Among these instabilities the transition from laminar flow to vortex shedding carries significant practical importance. Here we study a flow, where at high enough flow rates, vortices are generated by a fixed obstacle (cylinder), which penetrates a flowing, quasi-two dimensional soap film. We present experimental results that demonstrate that the transition from laminar flow to a periodic Kármán vortex street can be hysteretic, i.e. changing the mean flow rate $\bar V$ vortices c…
We provide a minimal model for an active nematic film in contact with both a solid substrate and a passive isotropic fluid, and explore its dynamics in one and two dimensions using a combination of hybrid Lattice Boltzmann simulations and analytical calculations. By imposing nematic anchoring at the substrate while active flows induce a preferred alignment at the interface ("active anchoring"), we demonstrate that directed fluid flow spontaneously emerges in cases where the two anchoring types are opposing. In one dimension, our model reduces to an analogue of a loaded elastic column. Here, th…
We study the interaction of two parallel rigid cylinders on the surface of a thin elastic film supported on a pool of liquid. The excess energy of the surface due to the curvature of the stretched film induces attraction of the cylinders that can be quantified by the variation of their gravitational potential energies as they descend into the liquid while still floating on the film. Although the experimental results follow the trend predicted from the balance of the gravitational and elastic energies of the system, they are somewhat underestimated. The origin of this discrepancy is the hystere…
An experimental investigation is reported on the effect of shear on the bursting of molten ultra-thin polymer films embedded in an immiscible matrix. By using an optical microscope coupled with a shearing hotstage, the dewetting dynamics, i.e. the growth of dewetting holes is monitored over time at various shear rates. It is observed that their circularity is modified by shear and that for all temperatures and thicknesses studied, the growth speed of the formed holes rapidly increases with increasing shear rate. A model balancing capillary forces and viscous dissipation while taking into accou…
Drying of colloidal droplets on solid, rigid substrates is associated with a capillary pressure developing within the droplet. In due course of time, the capillary pressure builds up due to droplet evaporation resulting in the formation of a colloidal thin film that is prone to crack formation. In this study, we show that introducing a minimal amount of nematic liquid crystal (NLC) can completely suppress the crack formation. The mechanism behind the curbing of the crack formation may be attributed to the capillary stress-absorbing cushion provided by the elastic arrangements of the liquid cry…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible low-Reynolds-number fluid or displacements in a two-dimensional linearly elastic solid seem to diverge logarithmically with the distance from the force center, which has led to some debate. Recently, we have demonstrated that such divergences cancel when the total (net) force vanishes. Here, we illustrate that, if a net force is present, the boundaries play a prom…
We present a method to probe molecular and nanoparticle diffusion within thin, solvated polymer coatings. The device exploits the confinement with well-defined geometry that forms at the interface between a planar and a hemi-spherical surface (of which at least one is coated with polymers) in close contact, and uses this confinement to analyse diffusion processes without interference of exchange with and diffusion in the bulk solution. With this method, which we call plane-sphere confinement microscopy (PSCM), information regarding the partitioning of molecules between the polymer coating and …
